Gregory;
1) "Will the locktite pull into the crack by capillary action?"
Not sure what it is, I don't think it's capillary action. The stuff is just so thin (low viscosity) that it will fill the cracks by itself (it just runs into the crack). Be careful with it - It's so thin that it will tend to run all over the place, so have a paper towel handy and apply VERY sparingly. You don't need much to fill those cracks.
2) "Do I fill the cracks while the bow is strung or unstrung?"
Since the cracks are vertical, it doesn't seem that it would make a difference. I think the cracks are from some lateral convexing caused by .... who knows. I would do it unstrung, but if you think they open more when strung - do it. I don't think it will hurt. Consider gluing when strung then unstring it before it dries. LT420 dries pretty quickly, so you don't have much time.
btw - LT420 is not generally available at a common hardware store. Try places similar to Grainger’s. (It's also a little expensive)
3) "Also what would you suggest for cleaning the excess epoxy?"
Scrape it off with a knife / sharp wood chisel, then sand or scrape the limb to the glass from the overlay down past the stress cracks an inch or two. You can scrape the old finish off (I use an old carving knife. Hold it laterally and pull-scrape the finish off. Hold the knife so the back of the blade is tilted toward you a little) then go to 220 and 320 grit paper. Be careful not to gouge the glass with the knife. Only remove the epoxy & the finish, NOT glass. Also, don't sand deeper than the finish layer on the limb glass. (You can sand into the glass just a little but not much). Feather out the transition from the bare glass at the cracks to the old finish about an inch or so past the ends of the stress cracks.
You might try filling the gap between the overlay and the limb with LT when strung also. I would mask the sides of the limb off good to prevent the LT from running back onto the wedge and the riser though. Recommend you mask it, glue it and clamp it. You should dry test your process on this before you start.
Good luck - Al